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Hahn-Banach Type Theorems for Locally Convex Cones

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

Walter Roth
Walter Roth
Affiliation:
Department of Mathematics Faculty of Science University Brunei DarussalamBandar Seri Begawan 2028 Brunei Darussalam e-mail: roth@ubd.edu.bn
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Abstract

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We prove Hahn-Banach type theorems for linear functionals with values in R∪{+∞} on ordered cones, Using the concept of locally convex cones, we provide a sandwich theorem involving sub- and superlinear functionals which are allowed to attain infinite values. It render general versions of well-known extension and separation results. We describe the range of all linear functionals sandwiched between given sub- and superlinear functionals on an ordered cone. The results are of interest even in vector spaces, since we consider sublinear functionals that may attain the value +∞.

Keywords

Hahn-Banach type theoremslocally convex cones

MSC classification

Secondary: 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators 46A03: General theory of locally convex spaces 46A20: Duality theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 1 , February 2000 , pp. 104 - 125
Copyright
Copyright © Australian Mathematical Society 2000

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